In words, a policy is a control strategy, that, at each time, decides the control action based on the history of the path. The adversary represents the environment: once the control action is taken, the adversary resolves the uncertainty stemming from the transition probability intervals, thus fixing the -still stochastic- environment for the current time step. Notice that, given a specific policy \(\pi \)  and adversary \(\xi \) , the caIMDP collapses to a time-varying Markov chain. Thus, given \(\pi \) , \(\xi \) , an initial state \(q_0\) , and a horizon \(N\) , a probability measure is uniquely defined over \((N+1)\) -length paths \(\omega \in \mathit {Paths}^{\mathrm {fin}}\)  [1]}.
